@Tanner write API could help with that, but until then, here's the high-level implementation/workaround:
FTPP (form-to-post plugin) establishes new POST route at /feedback
When that route is called, take req.body.text (where text is the id in the corresponding form) and call Topic.post as a pre-registered user.
That's pretty much it. There's more to expand on (such as spam prevention/throttling/auth/security), but yeah.